1. Field of the Invention
The invention is related generally to the field of interpretation of measurements made by well logging instruments for the purpose of determining the properties of earth formations. More specifically, the invention is related to a method for determination of anisotropic formation resistivity in a deviated wellbore using multifrequency, multicomponent resistivity data.
2. Background of the Art
Electromagnetic induction and wave propagation logging tools are commonly used for determination of electrical properties of formations surrounding a borehole. These logging tools give measurements of apparent resistivity (or conductivity) of the formation that when properly interpreted are diagnostic of the petrophysical properties of the formation and the fluids therein.
The physical principles of electromagnetic induction resistivity well logging are described, for example, in, H. G. Doll, Introduction to Induction Logging and Application to Logging of Wells Drilled with Oil Based Mud, Journal of Petroleum Technology, vol. 1, p. 148, Society of Petroleum Engineers, Richardson Tex. (1949). Many improvements and modifications to electromagnetic induction resistivity instruments have been devised since publication of the Doll reference, supra. Examples of such modifications and improvements can be found, for example, in U.S. Pat. No. 4,837,517; U.S. Pat. No. 5,157,605 issued to Chandler et al, and U.S. Pat. No. 5,452,761 issued to Beard et al.
A limitation to the electromagnetic induction resistivity well logging instruments known in the art is that they typically include transmitter coils and receiver coils wound so that the magnetic moments of these coils are substantially parallel only to the axis of the instrument. Eddy currents are induced in the earth formations from the magnetic field generated by the transmitter coil, and in the induction instruments known in the art these eddy currents tend to flow in ground loops which are substantially perpendicular to the axis of the instrument. Voltages are then induced in the receiver coils related to the magnitude of the eddy currents. Certain earth formations, however, consist of thin layers of electrically conductive materials interleaved with thin layers of substantially non-conductive material. The response of the typical electromagnetic induction resistivity well logging instrument will be largely dependent on the conductivity of the conductive layers when the layers are substantially parallel to the flow path of the eddy currents. The substantially non-conductive layers will contribute only a small amount to the overall response of the instrument and therefore their presence will typically be masked by the presence of the conductive layers. The non-conductive layers, however, are the ones that are typically hydrocarbon bearing and are of the most interest to the instrument user. Interpreting a well log made using the electromagnetic induction resistivity well logging instruments known in the art therefore may overlook some earth formations that might be of commercial interest.
The effect of formation anisotropy on resistivity logging measurements has long been recognized. Kunz and Moran studied the anisotropic effect on the response of a conventional logging device in a borehole perpendicular to the bedding plane of t thick anisotropic bed. Moran and Gianzero extended this work to accommodate an arbitrary orientation of the borehole to the bedding planes.
Rosthal (U.S. Pat. No. 5,329,448) discloses a method for determining the horizontal and vertical conductivities from a propagation or induction well logging device. The method assumes the angle between the borehole axis and the normal to the bedding plane, is known. Conductivity estimates are obtained by two methods. The first method measures the attenuation of the amplitude of the received signal between two receivers and derives a first estimate of conductivity from this attenuation. The second method measures the phase difference between the received signals at two receivers and derives a second estimate of conductivity from this phase shift. Two estimates are used to give the starting estimate of a conductivity model and based on this model, an attenuation and a phase shift for the two receivers are calculated. An iterative scheme is then used to update the initial conductivity model until a good match is obtained between the model output and the actual measured attenuation and phase shift.
Hagiwara (U.S. Pat. No. 5,656,930) shows that the log response of an induction-type logging tool can be described by an equation of the form                     V        ∝                              i                          L              3                                ⁢                      (                                                            -                  2                                ⁢                                                      ⅇ                                          ⅈ                      ⁢                                              xe2x80x83                                            ⁢                      k                      ⁢                                              xe2x80x83                                            ⁢                      L                                                        ⁡                                      (                                          1                      -                                              i                        ⁢                                                  xe2x80x83                                                ⁢                        k                        ⁢                                                  xe2x80x83                                                ⁢                        L                                                              )                                                              +                              i                ⁢                                  xe2x80x83                                ⁢                k                ⁢                                  xe2x80x83                                ⁢                                  l                  ⁡                                      (                                                                  ⅇ                                                  ⅈ                          ⁢                                                      xe2x80x83                                                    ⁢                          k                          ⁢                                                      xe2x80x83                                                    ⁢                          β                                                                    -                                              ⅇ                                                  ⅈ                          ⁢                                                      xe2x80x83                                                    ⁢                          k                          ⁢                                                      xe2x80x83                                                    ⁢                          L                                                                                      )                                                                        )                                              (        1        )            
where
xcex22=cos2xcex8+xcex2 sin2xcex8xe2x80x83xe2x80x83(2)
and
k2=xcfx892xcexc(∈h+i"sgr"h/xcfx89)xe2x80x83xe2x80x83(3)
where L is the spacing between the transmitter and receiver, k is the wavenumber of the electromagnetic wave, xcexc is the magnetic permeability of the medium, xcex8 is the deviation of the borehole angle from the normal to the formation, xcex is the anisotropy factor for the formation, xcfx89 is the angular frequency of the electromagnetic wave, "sgr"h is the horizontal conductivity of the medium and ∈h is the horizontal dielectric constant of the medium.
Eq. (3) is actually a pair of equations, one corresponding to the real part and one corresponding to the imaginary part of the measured signal, and has two unknowns. By making two measurements of the measured signal, the parameters k and xcex2 can be determined. The two needed measurements can be obtained from (1) R and X signals from induction logs, (2) phase and attenuation measurements from induction tools, (3) phase or attenuation measurements from induction tools with two different spacings, or (4) resistivity measurements at two different frequencies. In the low frequency limit, ∈ can be neglected in Eq. (3) and from known values of xcfx89 and xcexc, the conductivity "sgr" can be determined from k, assuming a value of xcexc equal to the permittivity of free space.
Wu (U.S. Pat. No. 6,092,024) recognized that the solution to eqs. (1)-(3) may be non-unique and showed how this ambiguity in the solution may be resolved using a plurality of measurements obtained from multiple spacings and/or multiple frequencies.
One solution to the limitation of the induction instruments known in the art is to include a transverse transmitter coil and a transverse receiver coil on the induction instrument, whereby the magnetic moments of these transverse coils is substantially perpendicular to the axis of the instrument. Such as solution was suggested in Tabarovsky and Epov, xe2x80x9cGeometric and Frequency Focusing in Exploration of Anisotropic Seamsxe2x80x9d, Nauka, USSR Academy of Science, Siberian Division, Novosibirsk, pp. 67-129 (1972). Tabarovsky and Epov suggest various arrangements of transverse transmitter coils and transverse receiver coils, and present simulations of the responses of these transverse coil systems configured as shown therein. Tabarovsky and Epov also describe a method of substantially reducing the effect on the voltage induced in transverse receiver coils which would be caused by eddy currents flowing in the wellbore and invaded zone. The wellbore is typically filled with a conductive fluid known as drilling mud. Eddy currents that flow in the drilling mud can substantially affect the magnitude of voltages induced in the transverse receiver coils. The wellbore signal reduction method described by Tabarovsky and Epov can be described as xe2x80x9cfrequency focusingxe2x80x9d, whereby induction voltage measurements are made at more than one frequency, and the signals induced in the transverse receiver coils are combined in a manner so that the effects of eddy currents flowing within certain geometries, such as the wellbore and invasion zone, can be substantially eliminated from the final result. Tabarovsky and Epov, however, do not suggest any configuration of signal processing circuitry which could perform the frequency focusing method suggested in their paper.
Strack et al. (U.S. Pat. No. 6,147,496) describe a multicomponent logging tool comprising a pair of 3-component transmitters and a pair of 3-component receivers. Using measurements made at two different frequencies, a combined signal is generated having a reduced dependency on the electrical conductivity in the wellbore region. U.S. Pat. No. 5,781,436 to Forgang et al, the contents of which are fully incorporated herein by reference, discloses a suitable hardware configuration for multifrequency, multicomponent induction logging.
U.S. Pat. No. 5,999,883 issued to Gupta et al, (the xe2x80x9cGupta patentxe2x80x9d), the contents of which are fully incorporated here by reference, discloses a method for determination of an initial estimate of the horizontal and vertical conductivity of anisotropic earth formations. Electromagnetic induction signals induced by induction transmitters oriented along three mutually orthogonal axes are measured at a single frequency. One of the mutually orthogonal axes is substantially parallel to a logging instrument axis. The electromagnetic induction signals are measured using first receivers each having a magnetic moment parallel to one of the orthogonal axes and using second receivers each having a magnetic moment perpendicular to a one of the orthogonal axes which is also perpendicular to the instrument axis. A relative angle of rotation of the perpendicular one of the orthogonal axes is calculated from the receiver signals measured perpendicular to the instrument axis. An intermediate measurement tensor is calculated by rotating magnitudes of the receiver signals through a negative of the angle of rotation. A relative angle of inclination of one of the orthogonal axes that is parallel to the axis of the instrument is calculated, from the rotated magnitudes, with respect to a direction of the vertical conductivity. The rotated magnitudes are rotated through a negative of the angle of inclination. Horizontal conductivity is calculated from the magnitudes of the receiver signals after the second step of rotation. An anisotropy parameter is calculated from the receiver signal magnitudes after the second step of rotation. Vertical conductivity is calculated from the horizontal conductivity and the anisotropy parameter. One drawback in the teachings of Gupta et al is that the step of determination of the relative angle of inclination of the required measurements of three components of data with substantially identical transmitter-receiver spacings. Because of limitations on the physical size of the tools, this condition is difficult to obtain; consequently the estimates of resistivities are susceptible to error. In addition, due to the highly nonlinear character of the response of multicomponent tools, such inversion methods are time consuming at a single frequency and even more so at multiple frequencies.
Analysis of the prior art leads to the conclusion that known methods of determining anisotropic resistivities in real time require very low frequencies; as a consequence of the low frequencies, the signal-to-noise ratio in prior art methods is quite low.
Co-pending U.S. patent application Ser. No. 09/825,104, (referred to hereafter as the ""104 application) filed on Apr. 3, 2001 teaches a computationally fast method of determination of horizontal and vertical conductivities of subsurface formations using a combination of data acquired with a transverse induction logging tool such as the 3DEXSM tool and data acquired with a conventional high definition induction logging tool (HDIL). The data are acquired in a vertical borehole. The HDIL data are used to determine horizontal resistivities that are used in an isotropic model to obtain expected values of the transverse components of the 3DEXSM. Differences between the model output and the acquired 3DEXSM data are indicative of anisotropy and this difference is used to derive an anisotropy factor. The method described therein has difficulties in deviated boreholes as the HDIL measurements used to derive the isotropic model are responsive to both horizontal and vertical resistivity.
There is a need for a fast and robust method of determination of anisotropic resistivity. Such a method should preferably be able to use high frequency measurements that are known to have better signal-to-noise ratio than low frequency methods. The present invention satisfies this need.
A method of logging subsurface formations using data acquired with a transverse induction logging tool, the formation having a horizontal conductivity and a vertical conductivity, by obtaining a plurality of frequencies measurements indicative of vertical and horizontal conductivities in a tool referenced coordinate system. The data are transformed to a subsurface formation coordinate system. Multifrequency focusing is applied to the measurements at a plurality of frequencies. Horizontal formation conductivities are determined from a subset of the focused conductivity measurements. Vertical formation conductivities are determined from the focused conductivity measurements associated with the subsurface formation and the horizontal conductivities.
In a preferred embodiment of the invention, a transformation independent of the formation azimuth may be used to determine the conductivity of the transversely anisotropic formation.